Artificial Neural Networks - Question about hidden layers.

[Atheist]

Hey.
Some background:
I have finished implementing an artificial neural network (ANN, with the help of articles, my beloved AI book, and some pre-existing code).
I do not yet know if my implementation is 100% correct, so I am doing tests to see if it is.
I have given the net very simple training data as such:
{5.0, 0.0, 0.0} -> "A"
{0.0, 5.0, 0.0} -> "B"
{0.0, 0.0, 5.0} -> "C"

It seems to be able to learn these patterns alright. The network I used for testing this was a very simple one, 3 input neurons and 3 output neurons. No hidden layers.

What I'm trying to do now:
Now I'm trying to train my network on something similar to above. I'm giving it images of every letter in the English alphabet (+ space and 0-9), in an attempt to later have it recognize letters in an image.

The problem:
Given that each image of a letter is 8x10 in size, im setting my ANN to have 80 input nodes, one for each pixel. There are 36 different characters that it will train on, so I let the ANN have 36 output nodes.
My problem is; How many hidden layers should I use? And what should the sizes of these hidden layers be? Is there a rule of thumb that one should use?
Its practically impossible for me to "try" a bunch of settings, given the time it actually takes to train these networks. (or perhaps the slowness is due to my implementation? I know training ANNs are slow, but this is almost unbearable!)

I'm grateful for any tips on this.
Thanks.